Passivity

A device is passive if it does not generate energy. This is a stronger condition than stability: not all stable models are passive. In the context of electromagnetic/circuit simulations, the quantities typically modeled are scattering (or S) parameters. These parameters are arranged in a square matrix that maps the incident wave amplitudes to the scattered wave amplitudes. For a passive device, the total power scattered by the device must be no greater than the power incident on it. Mathematically, this condition implies that the 2-norm, or equivalently, the maximum singular value, of the S-parameter matrix must be ≤1, for all frequencies.

Note that a model must be passive even outside the band of frequencies for which data is available. When a non-passive device is introduced into a circuit simulation, the simulation results may diverge for a bounded input, even if the device is stable. A typical case in which this occurs is when the non-passive device is part of a feedback loop. When modeling passive devices, it is important to ensure that the model is passive. Enforcing the passivity constraint is done in a separate step, after a state-space model has been generated. If the model is found to be non-passive, it is perturbed so as to make it passive. This is a complicated and quite computationally demanding step. Ansys has developed several algorithms for enforcing passivity. At the time of writing, passivity enforcement is not on by default. In many cases, a passive fit is obtained even if passivity is not enforced. Moreover, even if the fit is slightly non-passive, the time-domain simulation may still run fine. So the current logic is that, by default, the fits are initially done without passivity enforcement, the time-domain simulation is run, and if the results diverge, then passivity is enforced and the simulation is run again.